Simultaneous Identification Problem For Multiple Parameters In A Time-fractional Diffusion/diffusion-wave Equation

This paper deals with simultaneous identification problem of three parameters in a one-dimensional time-fractional diffusion/diffusion-wave equation.That is,we simultaneously recover the time fractional order,diffusion coefficient,and absorption coefficient using additional left endpoint measurements.Based on the series expression of the solution of the forward problem,we establish the uniqueness and existence of the classical solution to the forward problem and the uniqueness of the inverse problem.In this paper,the inverse problem is solved numerically using a trust region method.Numerical examples are presented for demonstrating the effectiveness of the numerical method and confirm the theoretical results.